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Nov 1976

Volume 60, Issue S1, pp. S1-S125

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back to top Session GG. Shock and Vibration IV
Contributed Papers
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Antisymmetric modes of vibration of a circular plate elastically restrained against rotation and subjected to a hydrostatic state of in‐plane stress (A)

P. A. A. Laura, L. E. Luisoni, and A. Arias

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S73-S73 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The analysis of flexural vibrations of plates with edges elastically restrained against rotation is of interest to the design engineer since ideal supports or clamps are difficult to obtain in practice. A survey of the literature reveals that several investigations have been performed in the past on (a) vibrating circular edges (without in‐plane loading) and (b) vibrating simply supported and clamped circular plates subjected to hydrostatic in‐plane loading. The present paper deals with the determination of very simple, approximate frequency equations which allow prediction of natural frequencies in the case of a vibrating circular plate which executes antisymmetric modes. It is shown that use of simple polynomial expression and a variational approach leads, in some cases, to numerical values which are more accurate than those available in the technical literature. The approach followed in the present investigation can be extended in a straightforward fashion to the case where the edge has translational flexibility.
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Vibrations of prolate spheroidal shells of constant thickness (A)

Courtney B. Burroughs and Edward B. Magrab

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S73-S73 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The general displacement‐equilibrium equations, which include the effects of transverse shear and rotary inertia, have been derived for a prolate spheroidal shell of constant thickness. The solution is formulated for a shell that is immersed in an inviscid fluid of infinite extent and subjected to an harmonically time‐varying, arbitrarily spatially distributed force normal to the shell surface. The approximate formal solutions for the three displacements of the shell surface and the two rotations of the shell cross section are obtained using an extension of Galerkin's variational method developed by Chi and Magrab [Proceedings of the International Conference on Variational Methods in Engineering (University of Southampton, 1974)]. Numerical results are presented for the lowest seven axisymmetric natural frequencies of the shell in vacuo. Using 15‐term solutions for both thick and thin shells, which have eccentricities that vary from 0.46 to 0.99, the approximate natural frequencies are found to converge to within less than 1% their final value. Good agreement with other published results for the approximate natural frequencies of a thin prolate spheroidal shell and for the exact natural frequencies of a thick spherical shell is obtained. Additional results for the natural frequencies of moderately thick shells as a function of shell eccentricity, mode number, and shell thickness are presented.
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Flexural waves generated in glass fibers by fracture (A)

P. G. Simpkins

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S73-S73 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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In 1948 Davies noted that flexural waves could be created in a rod by an unsymmetrical lead applied to one end. Miklowitz applied this observation to the hypothesis that during tensile fracture a moment pulse is exerted on the specimen which generates a flexural wave. He went on to suggest that this flexural wave could augment the stress induced in the rod by a reflected longitudinal wave when the two were coincident; thereby causing the secondary failures observed in brittle materials. The nature of the failure in fused silica fibers qualitatively suggests that it alters as the strength increases. While the low‐strength fibers simply fracture at one point, the high strength fibers (UTS > 2.8 GN/m2) appear to disintegrate into a particulate cloud. Recent photographic studies show that a flexural wave emanates from the primary fracture. When the strength is sufficient this flexural wave causes secondary explosive failures at other points along the fiber. These result in a particulate cloud of debris as the fiber appears to be progressively pulverized. Observations of the flexural wave amplitude show it to be a strong function of fiber strength. The observed group velocity of the flexural waves compares favorably with the classical time harmonic theories and the first‐mode Timoshenko approximation.
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Time‐average holographic study of a singing wine glass (A)

R. Tonin and D. A. Bies

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S73-S73 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Previous attempts to determine the motion of a free edge vibrating cylinder using time average optical holography have been inconclusive. On the assumption of strictly radial motion attempts at the interpretation of the fringes produced in orthogonal views has lead to the contradiction that the implied motion motion was not single valued [S. D. Liem et al., J. Sound Vib. 29, 475–481 (1973)]. In the latter reference it was suggested that the problem lay with the physical location of the optical fringes in the reconstructed image. However, as already shown by Rayleigh the motion of the free edge of a vibrating cylinder has both radial and tangential components of displacement and this point had not been taken into account. In this paper it is shown how the theory of time‐average optical holography may be extended to account for generalized elliptic motion of a vibrating surface under study and how the optical system may be arranged to unambiguously interpret the motion. It is shown that good argument is obtained between the predicted and observed motion for a singing wine glass and for a free edge rectangular cylinder vibrating in a Love mode.
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Vibrations of two concentric cylindrical shells containing a viscous fluid (A)

T. T. Yeh and S. S. Chen

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S73-S74 (1976); (2 pages)

Online Publication Date: 11 Aug 2005

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This study was motivated by the need to design the thermal shield in reactor internals to avoid detrimental flow‐induced vibrations. The system component is modeled as two coaxial shells separated by a viscous fluid. In the analysis, Flugge's shell equations of motion and linearized Navier‐Stokes equation for viscous fluid are employed. First, a traveling‐wave‐type solution is taken for shells and fluid. Then, from the interface conditions between the shells and fluid, the solution for the fluid medium is expressed in terms of shell displacements. Finally, using the shell equations of motion given the frequency equation, from which the natural frequency mode shape, and modal damping ratio of coupled modes can be calculated. Some important conclusions are as follows: (1) There exist structural modes and acoustic modes. If the structural natural frequencies and mode shapes are of primary interest, the fluid may be considered inviscid and incompressible. (2) There exist out‐of‐phase and in‐phase modes. The lowest natural frequency is always associated with the out‐of‐phase mode. (3) The lowest natural frequency of coupled modes are lower than the uncoupled modes. (4) The fluid viscosity contributes significantly to the modal damping.
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On the forced responses of damped cylindrical shells filled with pressurized liquid (A)

Y. P. Lu

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S74-S74 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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An analytical formulation for the forced vibratory responses of a pressurized liquid‐filled cylindrical shell having a number of mass segments adhered to it by a viscoelastic material is presented. The mass segments are discretely distributed around the outer circumference at an arbitrary section of the shell, and the excitation is a concentrated vibratory radial force located on the surface of the shell. The end conditions of the shell are assumed simply supported. The liquid is considered as a compressible and inviscid fluid. The viscoelastic material is assumed incompressible. The interaction between the shell and the attached mass segments, and the interaction between the shell and the enclosed liquid are taken into consideration. The driving point mechanical impedances at a location midway between two mass segments and half the distance along the length for a given damped system with or without pressurized water are given. These solutions are compared and discussed, respectively, with those of an undamped shell. The responses of a discontinuously constrained damped ring configuration without liquid enclosed and the frequencies of an undamped shell with pressurized water filled, which are the special cases derived from the analysis presented, are, respectively, compared very well with the available experimental data.
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Loss and coupling loss factors of two coupled dynamic systems (A)

G. Maidanik and J. E. Brooks

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S74-S74 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The Statistical Energy Analysis (SEA) has been employed to define and estimate the response of complex dynamic systems. Often a complex dynamic system is conveniently divided into a number of subsystem—basic dynamic systems. The complex is then modeled in terms of a number of coupled (basic) dynamic systems. Within the format of SEA the descritpion of the model is given in terms of the loss and coupling loss factors of the dynamic systems that compose the complex, Thus, to define the model, means must be devised to obtain the values of the loss and coupling loss factors. In this paper the experimental methods for obtaining these values are considered and scrutinized. For the most part considerations are limited to a complex consisting of two dynamic systems; the elements of an extension to higher forms of complexes are, however, included. It is shown that to obtain experimentally the loss and coupling loss factors one is required to conduct not only steady state but also transient experiments. The role of the reverberation time determined in the transient experiments is of particular interest.
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Use of the complex dynamic shear stiffness of a visco‐elastic liquid to illustrate the origins of structural damping (A)

R. A. Ely

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S74-S74 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The same complex stiffness notation which causes damping of solids and structures to appear to be independent of frequency and dependent on amplitude is shown to have descriptions of frequency‐dependent, velocity‐dependent, viscous damping hidden within it. That revelation is consistent with recent papers which report that only a viscous component of structural damping need be measured or modelled mathematically. Those papers also report that viscous damping accounts for all of the energy loss from built‐up structures (as elementary dimensional analysis shows it must), This paper draws upon measured values of the dissipative and elastic components of the complex dynamic viscosity and stiffness of a viscoelastic liquid to illustrate conceptual continuity from damping in liquids to damping in solids.
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Response of nonclassically damped systems to random excitation (A)

C. D. Michalopoulos

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S74-S74 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The response to stationary random excitation of multidegree‐of‐freedom systems which do not possess classical normal modes is obtained using a matrix perturbation technique. It is assumed that the damping matrix [C] is such that the off‐diagonal elements of the matrix [Φ]T[C][Φ], where [Φ] is the modal matrix associated with the undamped system, are small compared to its diagonal elements. General expressions for the correlation and spectral density matrices of the response are given. Examples of systems with two degrees of freedom are presented considering first and second orders of perturbation.
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Identification of natural frequencies and modal damping ratios from response data (A)

C. D. Michalopoulos

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S74-S74 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Response data are processed in the frequency domain to determine natural frequencies and modal damping ratios of a multidegree‐of‐freedom system. The excitation can be either deterministic or a random function of time. When the time history of the excitation is now known, the method requires its power spectral density to be flat. An iterative scheme is employed to minimize a mean‐square error function between the theoretical and measured power spectral densities of the response. In processing random response data, special steps are taken to minimize the statistical error. [Work supported by NASA.]
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Errors in power spectral density estimates of vibration test data (A)

M. E. Austin

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S74-S74 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Estimates of power spectral densities obtained using time‐compression, swept‐filter spectral analyzers may contain errors due to assumptions regarding normality, randomness and symmetry of the data being processed. This paper considers possible errors in these estimates caused by various effects. The first concern is for hidden periodic components in data records assumed to be entirely random. Expressions describing this error are developed. Also of concern are nonlinear effects in the instrumentation which may result in amplitude‐limiting of data records. Error analysis is performed for several possible amplitude distributions. Finally errors due to asymmetrical data records are considered. Records which are not normally‐distributed in amplitude exhibit some degree of asymmetry and thus the power spectral density estimates obtained from these records will be in error. Expressions for power spectral density estimates of amplitude distributions other than normal are developed. These are compared with estimates obtained under the normal assumption. Also, general relationships regarding power spectral density estimates as a function of the skewness and kurtosis of the data record are discussed.
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Analytical simulation and experimental measurement of stress wave propagation in guided projectile structures (A)

D. M. Anderson, J. G. Hanse, and T. N. Helvig

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S75-S75 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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An analytical simulation and experimental measurement of stress wave propagation through a guided projectile structure was made and the results correlated through the use of fast Fourier transform (FFT) methods. Two guided projectile structures were simulated; one with and one without bolted joints such that signal attenuation across a joint could be evaluated. The analytical simulation consisted of a linearly elastic finite element structural model subjected to a time‐history force input and solved using SAP IV via direct integration of the coupled differential equations. The experimental measurements were made using a pulse‐testing technique wherein a structure was instrumented with accelerometers and impacted with a force input and the accelerometer response and force input measured. The resulting time history response data, whether analytical or experimental, was then analyzed using FFT methods to generate a frequency domain representation of the response signal for comparison. Results indicate finite element structural simulations of elastic stress wave propagation are a valid design tool for studying the noise characteristics of a structure being impacted with low order force inputs. [Work sponsored by Honeywell Independent Development Funding.]
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Synthesis methods for an antivibration filter that is required to support the source mass (A)

C. B. Putnam and R. O. Rowlands

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S75-S75 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Classical network synthesis theory, that was developed for the design of electrical filters terminated in a resistance, may be applied to the design of anti‐vibration mechanical filters, except when the filter has to support the source mass. A modified design method has been developed to produce a termination consisting of a damped spring. Two cases are considered: (1) when the mass of the source is small, it is incorporated in the design as the first reactive arm of the filter, and (2) when the mass is large, the design is first performed assuming the source mass to be the infinite and then modified to take into account the finite value of the mass. [Work supported by Naval Sea Systems Command.]
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Preliminary analysis of tracked vehicle dynamics (A)

A. G. Galaitsis, P. J. Remington, and T. Norris

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S75-S75 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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A simplified model has been adopted to describe the nonlinear track/sprocket and track/idler interaction of a tracked vehicle. The differential equations of motion were obtained through the Lagrangian formulation and the time history of displacements and forces were computed by finite difference techniques. The predicted forces and measured force‐to‐noise transfer functions were, subsequently, used to project the interior vehicle noise which compares favorably to date. [Work supported by U. S. Army Contract DAAD005‐76‐C‐0748.]
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